cp_gen function

Generate PARAFAC data sets, optionally with outliers

Generates nsim data sets according to the given parameters. If eps > 0, the specified fraction of random outliers of the identified by the parameter type type are added to the data sets.

cp_gen(
  I = 20,
  J = 20,
  K = 20,
  nsim = 200,
  nf = 3,
  noise = 0.05,
  noise1 = 0,
  Acol = TRUE,
  Bcol = TRUE,
  Ccol = TRUE,
  congA = 0.5,
  congB = 0.5,
  congC = 0.5,
  eps = 0,
  type = c("none", "bl", "gl", "og"),
  c1 = 10,
  c2 = 0.1,
  silent = FALSE
)

Arguments

• I: number of observations

• J: number of variables

• K: number of occasions

• nsim: number of data sets to generate

• nf: number of PARAFAC components

• noise: level of homoscedastic (HO) noise

• noise1: level of heteroscedastic (HE) noise

• Acol: whether to apply collinearity with factor congA to mode A

• Bcol: whether to apply collinearity with factor congB to mode B

• Ccol: whether to apply collinearity with factor congC to mode C

• congA: collinearity factor for mode A

• congB: collinearity factor for mode B

• congC: collinearity factor for mode C

• eps: fraction of outliers (percent contamination)

• type: type of outliers: one of "none" for no outliers (possible only of eps==0), "bl" for bad leverage points, "gl" for good leverage points and "og" for orthogonal outliers

• c1: parameter for outlier generation (c1=10 for type="bl"

  or type="gl" and c1=1 for type="og")

• c2: parameter for outlier generation (c2=0.1 for type="bl"

  or type="og" and c2=0 for type="gl")

• silent: whether to issue warnings

Returns

A list consisting of the following lists:

• As list of nsim matrices for the mode A
• Bs list of nsim matrices for the mode B
• Cs list of nsim matrices for the mode C
• Xs list of nsim PARAFAC data sets, each with dimension IxJxK
• Os list of nsim vectors containing the added outliers (if any)
• param list of parameters used for generation of the data sets

Examples

##  Generate one PARAFAC data set (nsim=1) with R=2 components (nf=2) and dimensions
 ##  50x10x10. Apply 0.15 homoscedastic noise and 0.10 heteroscedastic noise, apply 
 ##  collinearity with congruence factor 0.5 to all modes. Add 20% bad leverage points.

 library(rrcov3way)
 xdat <- cp_gen(I=50, J=100, K=10, nsim=1, nf=2,
     noise=0.15, noise1=0.10, Acol=TRUE, Bcol=TRUE, Ccol=TRUE,
     congA=0.5, congB=0.5, congC=0.5,
     eps=0.2, type="bl")
 names(xdat)

References

Todorov, V. and Simonacci, V. and Gallo, M. and Trendafilov, N. (2023). A novel estimation procedure for robust CANDECOMP/PARAFAC model fitting. Econometrics and Statistics. In press.

Tomasi, G. and Bro, R., (2006). A comparison of algorithms for fitting the PARAFAC model. Computational Statistics & Data Analysis 50 (7), 1700--1734.

Faber, N.M. and Bro, R. and Hopke, P.K. (2003). Recent developments in CANDECOMP/PARAFAC algorithms: A critical review. Chemometrics and Intelligent Laboratory Systems 65 , 119--137.